If 𝑓(𝑥) = 𝑥12 − 𝑥 and 𝑔(𝑥) = 2𝑥3 − 𝑥12 − 𝑥, find f(x) − g(x).
Question
If 𝑓(𝑥) = 𝑥12 − 𝑥 and 𝑔(𝑥) = 2𝑥3 − 𝑥12 − 𝑥, find f(x) − g(x).
Solution
To find f(x) - g(x), we need to subtract the function g(x) from f(x).
f(x) = x^12 - x g(x) = 2x^3 - x^12 - x
So, f(x) - g(x) = (x^12 - x) - (2x^3 - x^12 - x)
Now, we simplify the equation by combining like terms:
= x^12 - x - 2x^3 + x^12 + x = 2x^12 - 2x^3
So, f(x) - g(x) = 2x^12 - 2x^3.
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